Abstract:

Whereas quantum measurement theory has given rise to many studies and controversies, due to its implications on the interpretation of quantum mechanics, it is hardly mentioned in courses. We shall first present the measurement problem, an apparent contradiction between the expected properties of individual runs of a repeated measurement and the quantum theory, which only deals with statistical ensembles. We shall then analyse the dynamics of ideal measurement processes, which involve a coupling between the tested system and the apparatus. The macroscopic size of the latter plays a major role, and we must rely on quantum statistical mechanics. We shall illustrate this approach with a rather realistic solvable model, and shall exhibit the needed properties of the Hamiltonian. This use of quantum equations being still purely formal, should be supplemented with interpretative principles. We shall exhibit the weakest possible such principles required to solve the measurement problem and shall discuss the status of Born's rule and of von Neumann's reduction. The course will be based on the following references [1] An ensemble theory of ideal quantum measurement processes. Armen E. Allahverdyan, Roger Balian, Theo M. Nieuwenhuizen. [[draft version below]]. This text gathers the main ideas which will be presented in this course. It is the draft of a manuscript not yet in final form. (Disregard the underlined sentences, which are still discussed between the authors so as to reach a final form.) [2] Understanding quantum measurement from the solution of dynamical models. Armen E. Allahverdyan, Roger Balian, Theo M. Nieuwenhuizen Phys. Rep. 525 (2013) 1-166 [[arXiv:1107.2138, t11/166, 2 paper copies available for borrowing on the books display shelf near the librarian office, at IPhT]]. This text contains a review of the literature about measurement models (beyond the scope of this course), and the detailed solution of a specific model which serves to illustrate the ideas of [1]. These ideas were already present in this review, but they appear in a more elaborate and more explicit form in [1]. [3]Lectures on dynamical models for quantum measurements Theo M. Nieuwenhuizen, Marti Perarnau-Llobet, Roger Balian [[arXiv:1406.5178, t14/005]]. This is a course containing details about the derivations of [2]. Among the references included in [1] and [2], many can be studied for deepening this course, for instance F. David's presentation of the principles of quantum mechanics [[arXiv:1211.5627, t12/042]], and F. Laloë's book (also published in French) about its interpretations.

ref_1_DRAFT.pdf Affiche.pdf Complementary_Notes+Bibliography.pdf